Aberration theory made simple

192 Pages·2011·11.032 MB·English

by  Mahajan, Virendra N

Aberration Theory
Made Simple
Second Edition
Downloaded from SPIE Digital Library on 26 Feb 2012 to 14.139.159.162. Terms of Use: http://spiedl.org/terms
Downloaded from SPIE Digital Library on 26 Feb 2012 to 14.139.159.162. Terms of Use: http://spiedl.org/terms
Aberration Theory
Made Simple
Second Edition
Virendra N. Mahajan
Tutorial Texts in Optical Engineering
Volume TT93
Bellingham, Washington USA
Downloaded from SPIE Digital Library on 26 Feb 2012 to 14.139.159.162. Terms of Use: http://spiedl.org/terms
Library of Congress Cataloging-in-Publication Data

Mahajan, Virendra N.
Aberration theory made simple / Virendra N. Mahajan. -- 2nd ed.
p. cm. -- (Tutorial texts series ; v. TT93)
Includes bibliographical references and index.
ISBN 978-0-8194-8825-1
1. Aberration. 2. Imaging systems. 3. Geometrical optics. I. Title.
QC671.M34 2011
621.36--dc23
2011025097

Published by

SPIE
P.O. Box 10
Bellingham, Washington 98227-0010 USA
Phone: [phone]
Fax: [phone]
Email: [email protected]
Web: http://spie.org

Copyright © 2011 Society of Photo-Optical Instrumentation Engineers (SPIE)

All rights reserved. No part of this publication may be reproduced or distributed in any
form or by any means without written permission of the publisher.

The content of this book reflects the work and thought of the author(s). Every effort has
been made to publish reliable and accurate information herein, but the publisher is not
responsible for the validity of the information or for any outcomes resulting from reliance
thereon.

First printing

Printed in the United States of America.

Downloaded from SPIE Digital Library on 26 Feb 2012 to 14.139.159.162. Terms of Use: http://spiedl.org/terms
Introduction to the Series

Since its inception in 1989, the Tutorial Texts (TT) series has grown to cover
many diverse fields of science and engineering. The initial idea for the series was
to make material presented in SPIE short courses available to those who could
not attend and to provide a reference text for those who could. Thus, many of the
texts in this series are generated by augmenting course notes with descriptive text
that further illuminates the subject. In this way, the TT becomes an excellent
stand-alone reference that finds a much wider audience than only short course
attendees.
Tutorial Texts have grown in popularity and in the scope of material covered
since 1989. They no longer necessarily stem from short courses; rather, they are
often generated independently by experts in the field. They are popular because
they provide a ready reference to those wishing to learn about emerging
technologies or the latest information within their field. The topics within the
series have grown from the initial areas of geometrical optics, optical detectors,
and image processing to include the emerging fields of nanotechnology,
biomedical optics, fiber optics, and laser technologies. Authors contributing to
the TT series are instructed to provide introductory material so that those new to
the field may use the book as a starting point to get a basic grasp of the material.
It is hoped that some readers may develop sufficient interest to take a short
course by the author or pursue further research in more advanced books to delve
deeper into the subject.
The books in this series are distinguished from other technical monographs
and textbooks in the way in which the material is presented. In keeping with the
tutorial nature of the series, there is an emphasis on the use of graphical and
illustrative material to better elucidate basic and advanced concepts. There is also
heavy use of tabular reference data and numerous examples to further explain the
concepts presented. The publishing time for the books is kept to a minimum so
that the books will be as timely and up-to-date as possible. Furthermore, these
introductory books are competitively priced compared to more traditional books
on the same subject.
When a proposal for a text is received, each proposal is evaluated to
determine the relevance of the proposed topic. This initial reviewing process has
been very helpful to authors in identifying, early in the writing process, the need
for additional material or other changes in approach that would serve to
strengthen the text. Once a manuscript is completed, it is peer reviewed to ensure
that chapters communicate accurately the essential ingredients of the science and
technologies under discussion.
It is my goal to maintain the style and quality of books in the series and to
further expand the topic areas to include new emerging fields as they become of
interest to our reading audience.

James A. Harrington
Rutgers University
Downloaded from SPIE Digital Library on 26 Feb 2012 to 14.139.159.162. Terms of Use: http://spiedl.org/terms
To My
Wife Shashi Prabha
Son Vinit Bharati
Daughter Sangita Bharati
Downloaded from SPIE Digital Library on 26 Feb 2012 to 14.139.159.162. Terms of Use: http://spiedl.org/terms
FOREWORD TO THE FIRST EDITION
It is a distinct pleasure for me to write this short foreword to Dr. Virendra Mahajan's
tutorial text, Aberration Theory Made Simple. I write it not because I am particularly
knowledgeable about aberration theory—in fact, it may be because I am not particularly
knowledgeable that I was invited! This is a Tutorial Text, and as a lifelong educator I am
also a lifelong learner and I should be able to learn from this text; and I did.
This text is prepared in the ideal way for a tutorial. It comes as a direct result of
teaching this material to a wide range of audiences in a wide range of locations; so it has
been tried and tested. The "student guinea pigs" have performed their invaluable service
so that those of us who come along later have the benefit of their and the author's labors.
Dr. Mahajan has lived up to his title and made aberration theory simple. Of course, I
should caution the reader that simple is relative. Some topics do not yield easily to simple
yet accurate descriptions. Those readers who insist that "rays" are the most important
components of any analysis of optical systems, whether aberrant or not, will be very
satisfied with the first half of the book, but may wish to ignore the second half. They
should not. Those who are enamored with the wave approach (like me) will immediately
read the second half of this book and applaud, but not go back and read the first half.
They should! I did!
I am pleased that Dr. Mahajan has provided a significant list of references in addition
to the bibliography at the end of the book. This will be of considerable value to the
reader. Not incidentally, SPIE Optical Engineering Press will also publish a Milestone
volume on Effects of Aberrations in Imaging Systems with Dr. Mahajan as the editor.
Thus, each of us will be able to have an authoritative companion volume that contains
reprints from the world's literature that will no doubt verify that this current Tutorial Text
is indeed Aberration Theory Made Simple.
Brian J. Thompson June 1991
Rochester, New York
ix
Downloaded from SPIE Digital Library on 26 Feb 2012 to 14.139.159.162. Terms of Use: http://spiedl.org/terms
TABLE OF CONTENTS
ABERRATION THEORY MADE SIMPLE
Preface to the Second Edition .........................................................................................xv
Preface to the First Edition ..........................................................................................xvii
Symbols and Notation ....................................................................................................xxi
CHAPTER 1: OPTICAL ABERRATIONS ......................................................1
1.1 Introduction ............................................................................................................................1
1.2 Optical Imaging ......................................................................................................................1
1.3 Wave and Ray Aberrations ...................................................................................................3
1.4 Defocus Aberration ................................................................................................................5
1.5 Wavefront Tilt ........................................................................................................................7
1.6 Aberration Function of a Rotationally Symmetric System ................................................8
1.7 Effect of Change in Aperture Stop Position on the Aberration Function .......................10
1.8 Aberrations of a Spherical Refracting Surface .................................................................13
1.9 Aberration Function of a Multielement system .................................................................16
1.10 Summary ...............................................................................................................................17
Appendix: Sign Convention ..........................................................................................................18
CHAPTER 2: THIN LENS ...........................................................................19
2.1 Introduction ..........................................................................................................................19
2.2 Gaussian Imaging .................................................................................................................19
2.3 Primary Aberrations ............................................................................................................20
2.4 Spherical Aberration and Coma .........................................................................................21
2.5 Numerical Problems .............................................................................................................24
2.5.1 Thin Lens Focusing a Parallel Beam of Light .......................................................24
2.5.2 Aplanatic Doublet Focusing a Parallel Beam of Light ...........................................25
2.6 Summary ...............................................................................................................................26
CHAPTER 3: ABERRATIONS OF A PLANE-PARALLEL PLATE ...................27
3.1 Introduction ..........................................................................................................................27
3.2 Gaussian Imaging .................................................................................................................27
3.3 Primary Aberrations ............................................................................................................29
3.4 Numerical Problem ..............................................................................................................30
3.5 Summary ...............................................................................................................................30
xi
Downloaded from SPIE Digital Library on 26 Feb 2012 to 14.139.159.162. Terms of Use: http://spiedl.org/terms
CHAPTER 4: ABERRATIONS OF A SPHERICAL MIRROR ........................33
4.1 Introduction ..........................................................................................................................33
4.2 Primary Aberration Function .............................................................................................33
4.3 Aperture Stop at the Mirror ...............................................................................................35
4.4 Aperture Stop at the Center of Curvature of the Mirror .................................................36
4.5 Numerical Problems .............................................................................................................38
4.6 Summary ...............................................................................................................................41
CHAPTER 5: SCHMIDT CAMERA ............................................................43
5.1 Introduction ..........................................................................................................................43
5.2 Schmidt Plate ........................................................................................................................43
5.3 Numerical Problems .............................................................................................................49
5.4 Summary ...............................................................................................................................50
CHAPTER 6: ABERRATIONS OF A CONIC SURFACE .............................51
6.1 Introduction ..........................................................................................................................51
6.2 Conic Surface ........................................................................................................................51
6.3 Conic Refracting Surface .....................................................................................................52
6.3.1 On-Axis Point Object .............................................................................................52
6.3.2 Off-Axis Point Object ............................................................................................53
6.4 General Aspherical Refracting Surface .............................................................................55
6.5 Conic Reflecting Surface ......................................................................................................56
6.6 Paraboloidal Mirror .............................................................................................................56
6.7 Multimirror Systems ............................................................................................................56
6.8 Summary ...............................................................................................................................57
CHAPTER 7: RAY SPOT SIZES AND DIAGRAMS .....................................59
7.1 Introduction ..........................................................................................................................59
7.2 Wave and Ray Aberrations .................................................................................................59
7.3 Spherical Aberration ...........................................................................................................62
7.4 Coma ......................................................................................................................................64
7.5 Astigmatism ...........................................................................................................................66
7.6 Field Curvature ....................................................................................................................69
7.7 Astigmatism and Field Curvature ......................................................................................70
7.8 Distortion ...............................................................................................................................70
7.9 Spot Diagrams .......................................................................................................................71
7.10 Aberration Tolerance and a Golden Rule of Optical Design ...........................................72
7.11 Summary ...............................................................................................................................75
xii
Downloaded from SPIE Digital Library on 26 Feb 2012 to 14.139.159.162. Terms of Use: http://spiedl.org/terms
CHAPTER 8: SYSTEMS WITH CIRCULAR PUPILS ......................................77
8.1 Introduction ..........................................................................................................................77
8.2 Point-Spread Function (PSF) ..............................................................................................78
8.2.1 Aberrated PSF ........................................................................................................78
8.2.2 Aberration-Free PSF ...............................................................................................79
8.2.3 Rotationally Symmetric PSF ..................................................................................81
8.2.4 Defocused PSF .......................................................................................................81
8.2.5 Axial Irradiance ......................................................................................................82
8.3 Strehl Ratio ...........................................................................................................................83
8.3.1 General Expressions ...............................................................................................83
8.3.2 Primary Aberrations ...............................................................................................85
8.3.3 Balanced Primary Aberrations ...............................................................................85
8.3.4 Comparison of Approximate and Exact Results ....................................................86
8.3.5 Strehl Ratio for Nonoptimally Balanced Aberrations ............................................88
8.3.6 Rayleigh’s l 4 Rule .............................................................................................88
8.3.7 Balanced Aberrations and Zernike Circle Polynomials .........................................89
8.4 2D PSFs .................................................................................................................................92
8.5 Optical Transfer Function (OTF) .....................................................................................100
8.5.1 OTF and Its Physical Significance .......................................................................100
8.5.2 Aberration-Free OTF ............................................................................................101
8.5.3 Hopkins Ratio and Aberration Tolerance .............................................................103
8.5.4 Contrast Reversal .................................................................................................104
8.6 Summary .............................................................................................................................107
References ......................................................................................................................................109
CHAPTER 9: SYSTEMS WITH ANNULAR AND GAUSSIAN PUPILS .........111
9.1 Introduction ........................................................................................................................111
9.2 Annular Pupils ....................................................................................................................111
9.2.1 Aberration-Free PSF .............................................................................................111
9.2.2 Aberration-Free OTF ............................................................................................116
9.2.3 Axial Irradiance ....................................................................................................117
9.2.4 Strehl Ratio ...........................................................................................................119
9.2.5 Balanced Aberrations and Zernike Annular Polynomials ....................................125
9.3 Gaussian Pupils ..................................................................................................................126
9.3.1 Aberration-Free PSF .............................................................................................126
9.3.2 Aberration-Free OTF ............................................................................................130
9.3.3 Axial Irradiance ....................................................................................................131
9.3.4 Strehl ratio ............................................................................................................132
9.3.5 Balanced Aberrations and Zernike-Gauss Circle Polynomials ............................133
9.3.6 Weakly Truncated Pupils .....................................................................................135
9.4 Summary .............................................................................................................................137
References ......................................................................................................................................138
xiii
Downloaded from SPIE Digital Library on 26 Feb 2012 to 14.139.159.162. Terms of Use: http://spiedl.org/terms